Skip to main navigation Skip to main content Skip to page footer
Menu

Υ1204 - INTRODUCTION TO DIFFERENTIAL AND INTEGRAL CALCULUS AND STATISTICS

INSTRUCTORS

Lectures:

Ch. Tsitouras, Prof.

eClass Webpage

COURSE KEY ELEMENTS

LEVEL / SEMESTER:

EQF level 6; NQF of Greece level 6 / 1st

TYPE:

General background, Skill Development

TEACHING ACTIVITIES - HOURS/WEEK  - ECTS:

Lectures & tutorials
4 hours of lecturing,
2 hours of tutorials per week,
6 ECTS credit

Prerequisites:

None

Language of instruction and Assessment:

Greek

Availability to Erasmus+ Students:

NO

COURSE CONTENT:

Introduction to Differential and Integral Calculus

  • Basic definitions of matrices, matrix operations, matrix inverse, solving systems using inverses, determinants of matrices, properties of determinants, finding inverse matrix using adjoint, solving systems using Cramer's method, Eigenvalues and eigenvectors - definitions and properties, eigenspaces, Characteristic polynomial, matrix similarity, diagonalization, Cayley-Hamilton Theorem.
  • Derivative of a function, geometric interpretation, rules of derivation, derivative of a complex function, limit of a function, l'Hospital rules.
  • Indefinite integral- definition and properties, methods of integration.
  • Definite integral- definition and properties, calculation of definite integral, Generalized integrals, applications.
  • Functions of many variables. Partial derivative, higher order derivatives, calculation of partial derivatives.
  • Least squares method.
  • Double integral- definition and properties, calculation of double integral (Cartesian-polar coordinates), contour integral, applications.

Statistics

  • Sum principle, multiplicative principle, sample space, simple events (intersection, union and difference of events, complementary event, disjoined and independent events, De Morgan formulas), classical definition of Probability (Laplace), axiomatic definition of Probability (Kolmogorov) and properties, probability of complementary events, probability of union of events, conditional probability, Total Probability Theorem, Bayes formula, independence of events, probability of intersection of independent events.
  • Random variable, distribution function, probability density function, mean, variance, standard deviation, Poisson distribution, Normal distribution.
  • Random sample, sample mean, sample variance, confidence intervals, and hypothesis tests for the mean of the distribution of random sample data.

LEARNING ACTIVITIES - TEACHING METHODS:

PLANNED LEARNING ACTIVITIES:

Activity Student’s effort
Lectures78 hours
Individual Study/ Bibliography Analysis/ Preparation97 hours
Total student effort175 hours

ASSESSMENT METHODS AND CRITERIA

  • Final written exams in Greek (100%)

RECOMMENDED BIBLIOGRAPHY

Suggested  Bibliogrraphy:

  • General Mathematics (in Greek), Ch. Massouros, Ch. Tsitouras, ISBN: 9786185066512 [Eudoxus code: 59392755]

 

 

STUDY: